Question

Find the absolute minimum and absolute maximum of f(x,y)=14−7x+10y f(x,y)=14−7x+10y on the closed triangular region with vertices (0,0),(10,0)(0,0),(10,0) and (10,13)(10,13). List the minimum/maximum values as well as the point(s) at which they occur. If a min or max occurs at multiple points separate the points with commas.

Answer 1

Answer:

Maximum value of f(x,y) at (10,13)=74

Minimum value of f(x,y) at (10,0)=-56

Step-by-step explanation:

We are given that

$f(x,y)=14-7x+10y$

Vertices are (0,0),(10,0) and (10,13)

Substitute x=0 and y=0

$f(0,0)=14-0+0=14$

Substitute x=10 and y=0

$f(10,0)=14-7(10)+10(0)=14-70=-56$

Substitute x=10 and y=13

$f(10,13)=14-7(10)+10(13)=14-70+130=74$

Maximum value of f(x,y) at (10,13)=74

Minimum value of f(x,y) at (10,0)=-56